We introduce Simulation Streams, a programming paradigm designed to efficiently control and leverage Large Language Models (LLMs) for complex, dynamic simulations and agentic workflows. Our primary goal is to create a minimally interfering framework that harnesses the agentic abilities of LLMs while addressing their limitations in maintaining consistency, selectively ignoring/including information, and enforcing strict world rules. Simulation Streams achieves this through a state-based approach where variables are modified in sequential steps by "operators," producing output on a recurring format and adhering to consistent rules for state variables. This approach focus the LLMs on defined tasks, while aiming to have the context stream remain "in-distribution". The approach incorporates an Entity-Component-System (ECS) architecture to write programs in a more intuitive manner, facilitating reuse of workflows across different components and entities. This ECS approach enhances the modularity of the output stream, allowing for complex, multi-entity simulations while maintaining format consistency, information control, and rule enforcement. It is supported by a custom editor that aids in creating, running, and analyzing simulations. We demonstrate the versatility of simulation streams through an illustrative example of an ongoing market economy simulation, a social simulation of three characters playing a game of catch in a park and a suite of classical reinforcement learning benchmark tasks. These examples showcase Simulation Streams' ability to handle complex, evolving scenarios over 100s-1000s of iterations, facilitate comparisons between different agent workflows and models, and maintain consistency and continued interesting developments in LLM-driven simulations.